System of Linear Equations and Application of Garin–Lowry Model in Simulating Urban Population and Employment Patterns

This chapter introduces the method for solving a system of linear equations (SLE). The technique is used in many applications including the popular input-output analysis (see Appendix 10A for a brief introduction). The method is fundamental in numerical analysis (NA), and is often used as a building block in other NA tasks such as solving a system of nonlinear equations and the eigenvalue problem. Appendix 10B shows how the solution of a system of nonlinear equations utilizes the solution method of SLE.